Abstract
Classification is one of the basic tasks in machine learning, which aims to divide the input samples into several groups labeled by specific categories. Most traditional statistical classification methods are based on matrix computation. However, a large number of samples are multiway data like color images (third-order tensors) and videos (fourth-order tensors). We have to vectorize these data when using matrix computation-based classification methods, which could lead to the loss of information and overfitting problems. To address these issues, most of the classical classification methods can be extended to their tensor versions. In this chapter, we introduce a framework for this generalization. It replaces the linear hyperplane with the tensor form based tensor planes for classification. We take three typical classification methods to show how it can be generalized into their tensor versions, including logistic tensor regression, support tensor machine (STM), and tensor Fisher discriminant analysis. Although there are numerous data processing applications for tensor classification, we only show its effectiveness by digit recognition from visual images and compare a series of tensor classification methods by a group of experiments on biomedical classification from fMRI images.
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Notes
- 1.
For a real symmetric matrix A, the Rayleigh quotient is defined as \(\operatorname {R}(\mathbf {x}) = \frac {{\mathbf {x}}^{\mathrm {T}}\mathbf {A}\mathbf {x}}{{\mathbf {x}}^{\mathrm {T}}\mathbf {x}}\).
- 2.
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Liu, Y., Liu, J., Long, Z., Zhu, C. (2022). Statistical Tensor Classification. In: Tensor Computation for Data Analysis. Springer, Cham. https://doi.org/10.1007/978-3-030-74386-4_8
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DOI: https://doi.org/10.1007/978-3-030-74386-4_8
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